Question: Express your answer as a mixed number simplified to lowest terms. $8\dfrac{1}{10}-4\dfrac{2}{3} = {?}$
Explanation: Find a common denominator for the fractions: $= {8\dfrac{3}{30}}-{4\dfrac{20}{30}}$ Convert ${8\dfrac{3}{30}}$ to ${7 + \dfrac{30}{30} + \dfrac{3}{30}}$ So the problem becomes: ${7\dfrac{33}{30}}-{4\dfrac{20}{30}}$ Separate the whole numbers from the fractional parts: $= {7} + {\dfrac{33}{30}} - {4} - {\dfrac{20}{30}}$ Bring the whole numbers together and the fractions together: $= {7} - {4} + {\dfrac{33}{30}} - {\dfrac{20}{30}}$ Subtract the whole numbers: $=3 + {\dfrac{33}{30}} - {\dfrac{20}{30}}$ Subtract the fractions: $= 3+\dfrac{13}{30}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{13}{30}$